+ In the last chapter you met number sentences — short lines that use digits and + special marks, like 3 + 4 = 7. This chapter is a guide to those marks: what each + one is called, how to say it out loud, and what it tells you to do. You do not need to be fast at + arithmetic yet; you only need to read the symbols like words on a sign. +
+ ++ The symbols 0 through 9 are called digits. Each + digit stands for a counting amount (zero through nine). When you write a bigger number, you put + digits side by side with no gap: 47 means four tens and seven ones. +
++ A full line of math often mixes words (in your head or in a story) with + symbols (on paper). “Three plus four equals seven” is the same idea as + 3 + 4 = 7. +
+ +| Symbol | +Name | +Say it like this | +
|---|---|---|
| 0–9 | +digits | +“zero”, “one”, … “nine” | +
| (space) | +space between parts | +pause between numbers and signs so the line is easy to read | +
+ The plus sign looks like a small cross: +. It means + put together or add. +
++ Read 3 + 4 = 7 as: “three plus four equals seven.” You are + joining two groups into one total. +
+ +Remember
+The plus sign is not the letter “t”. It sits between the numbers you are combining.
++ The minus sign is a short horizontal line: − (sometimes written + as a hyphen - on a keyboard). It means take away or + subtract. +
++ Read 7 − 3 = 4 as: “seven minus three equals four.” Start with + seven things, remove three, and count what is left. +
+ +Minus or hyphen?
++ In a number sentence, the short line between numbers is a minus + sign. In ordinary writing, the same shape can join words (like “well-known”) — that + is a hyphen, not “take away.” Look at what is on each side: digits mean minus. +
++ The times sign looks like a tilted cross or letter x: ×. It + means multiply — many equal groups. +
++ Our main example is three groups of four makes twelve. You can spell that same + fact in several ways on paper: +
++ Read any of the lines above as: “three times four equals twelve,” or “three + groups of four.” +
+ ++ The division sign is a dot with a line: ÷. It means + split into equal groups or share fairly. +
++ Take twelve shared into four equal piles; each pile has three. Again, the same + fact can look different on the page: +
++ Read 12 ÷ 4 = 3 or 12/4 = 3 as: “twelve divided by four + equals three.” Twelve dots shared into four equal piles give three in each pile. +
++ A slash between two numbers is a quick way to write division or a fraction in one + line: 1/2 is “one half,” and 12/4 is the same sharing story as + twelve divided by four. In typeset math the numbers can sit one above the other: + \(\tfrac{1}{2}\) (one half) and \(\dfrac{12}{4} = 3\) (twelve over four equals three). +
+ ++ The equals sign is two parallel lines: =. It means + is the same amount as on both sides. +
++ Read a full sentence from left to right. In 5 + 2 = 7, the left side (five plus + two) has the same total as the right side (seven). The equals sign is the bridge between them. +
+ +One sentence
++ Treat the whole line as one idea: “five plus two equals seven.” Do not stop reading at the plus + sign — finish at the number after the equals sign. +
++ Round brackets — also called parentheses — wrap part of a + sentence: ( and ). They mean: do this group + first, then use the result with the rest of the line. +
++ In (2 + 3) + 4, add two and three inside the brackets to get five, then add four + to get nine. Without brackets, 2 + 3 + 4 still totals nine, but brackets help + when the order would be unclear. +
+ +| Symbol | +Name | +Meaning | +Example | +
|---|---|---|---|
| + | +plus | +put together | +3 + 4 = 7 | +
| − | +minus | +take away | +7 − 3 = 4 | +
| × | +times | +equal groups | +3 × 4 = 12 | +
| ÷ | +divided by | +fair shares | +12 ÷ 4 = 3 | +
| = | +equals | +same amount both sides | +5 + 2 = 7 | +
| ( ) | +brackets | +this part first | +(2 + 3) + 4 = 9 | +
+ Sometimes we compare two amounts without adding or subtracting. The open mouth of the symbol + points at the bigger number. +
++ You may also see ≤ (less than or equal) and ≥ (greater than or + equal). The extra line means “or the same amount.” +
+ ++ In big numbers like 1,000, a comma groups digits in threes so + the number is easier to read — one thousand, not “one zero zero zero” as separate ideas. +
++ A decimal point . sits between a whole part and a smaller part. + 3.50 might mean three dollars and fifty cents: the part after the point is not + whole dollars. You will learn more about decimals later; for now, remember the dot splits the + number into two pieces. +
+ ++ A fraction names part of a whole split into equal pieces. You + might see a single character like ½, or plain text with a slash + 1/2, or the same value written tall in math as \(\tfrac{1}{2}\) — all mean + one part out of two equal parts. +
++ The percent sign % means out of one hundred. + 50% means fifty out of every hundred — half of the whole. If a test has 100 + points and you score 80, you might say you got 80%. +
+ ++ Three dots in a row … (an ellipsis) mean the pattern keeps + going the same way: 2, 4, 6, 8, … — two, four, six, eight, and so on. +
++ The sign ≈ means approximately or about — close + but not exact. 10 ÷ 3 ≈ 3 is a rough answer; the exact value is a bit more than + three. +
+ ++ As you grow, books will add more symbols: a colon for ratios, small numbers + above the line for powers, and pairs of letters in graphs. You do not need them yet; this chapter + is enough to read everyday number sentences. +
+ ++ Say each line out loud before you calculate. Cover the answer with your hand, then check: +
++ People counted with fingers and words long before they agreed on one way to write math. Ancient + Egyptians and Babylonians used pictures and marks for amounts. Over centuries, different + countries used different symbols for the same ideas. +
++ The equals sign (=) was popularised in the 1500s by Welsh mathematician + Robert Recorde. He chose two lines because “no two things can be more equal” than + parallel lines — a way to show both sides match. +
++ The plus and minus signs (+ and −) became common in Europe + around the same era, replacing longer Latin words. The times sign (×) and + division sign (÷) appeared later, when printing books needed short, clear marks + that fit on one line. +
++ Brackets grew important when formulas got longer — mathematicians needed a visible rule for + “which part first,” just like you do in (2 + 3) + 4. +
+ ++ Writing “three plus four equals seven” every time is long. Symbols are a shorthand: + the same meaning in less space, so you can compare many sentences quickly. +
+ ++ If the left side of \(=\) counts to \(a\) and the right side counts to \(b\), then \(a = b\) + means both sides name the same number. If they were different, the sentence would + be false — like claiming \(3 + 4 = 8\) when seven dots are the true total. +
+ ++ Without a rule, \(2 + 3 \times 4\) could be read in two ways. Brackets fix one group: + \((2 + 3) \times 4 = 5 \times 4 = 20\). Later you will learn more order rules; for now, + brackets always mean “work inside first.” +
+ +Pause and answer in your head or with a partner.
+ +Checkpoint
+What is the name of the sign in \(7 - 3 = 4\)? What does it tell you to do?
+Checkpoint
+Say out loud: \(4 \times 2 = 8\). Which word goes with \(\times\)?
+Checkpoint
+In \((5 + 1) + 2\), which part do you work out first? What is the final total?
+Checkpoint
+Is \(6 > 2\) true? What does the open side of \(>\) point toward?
+Checkpoint
+What does \(50\%\) mean in words (“out of …”)?
+Answer: A cross-shaped mark + that means add or put together.
+Answer: “Five equals five.”
+Answer: Minus: − (or - on a keyboard).
+Answer: “Nine divided by three equals three.”
+Answer: Multiply — four groups of two (or two groups of four), total eight.
+Answer: \(9\).
+Steps: Inside brackets: \(3 + 2 = 5\). Then \(5 + 4 = 9\).
+Answer: True — four is less than nine.
+Answer: Seven is bigger. Examples: \(7 > 5\) or \(5 < 7\).
+Answer: One half — one part out of two equal parts.
+Answer: Twenty-five out of every hundred — a quarter of the price is taken off (you will learn to compute the exact dollars later).
+Answer: \((2 \times 3) + 1 = 7\). \(2 \times (3 + 1) = 2 \times 4 = 8\). They are not the same — brackets change the result.
+Explanation: Brackets show which group to do first; this is why notation matters.
+Answer: Dot \(\cdot\) and asterisk \(*\) (on keyboards/calculators).
+Answer: “One thousand plus five hundred equals one thousand five hundred.” The comma groups digits in threes to show thousands.
++ In the last chapter you met number sentences — short lines that use digits and + special marks, like 3 + 4 = 7. This chapter is a guide to those marks: what each + one is called, how to say it out loud, and what it tells you to do. You do not need to be fast at + arithmetic yet; you only need to read the symbols like words on a sign. +
+ ++ The symbols 0 through 9 are called digits. Each + digit stands for a counting amount (zero through nine). When you write a bigger number, you put + digits side by side with no gap: 47 means four tens and seven ones. +
++ A full line of math often mixes words (in your head or in a story) with + symbols (on paper). “Three plus four equals seven” is the same idea as + 3 + 4 = 7. +
+ +| Symbol | +Name | +Say it like this | +
|---|---|---|
| 0–9 | +digits | +“zero”, “one”, … “nine” | +
| (space) | +space between parts | +pause between numbers and signs so the line is easy to read | +
+ The plus sign looks like a small cross: +. It means + put together or add. +
++ Read 3 + 4 = 7 as: “three plus four equals seven.” You are + joining two groups into one total. +
+ +Remember
+The plus sign is not the letter “t”. It sits between the numbers you are combining.
++ The minus sign is a short horizontal line: − (sometimes written + as a hyphen - on a keyboard). It means take away or + subtract. +
++ Read 7 − 3 = 4 as: “seven minus three equals four.” Start with + seven things, remove three, and count what is left. +
+ +Minus or hyphen?
++ In a number sentence, the short line between numbers is a minus + sign. In ordinary writing, the same shape can join words (like “well-known”) — that + is a hyphen, not “take away.” Look at what is on each side: digits mean minus. +
++ The times sign looks like a tilted cross or letter x: ×. It + means multiply — many equal groups. +
++ Our main example is three groups of four makes twelve. You can spell that same + fact in several ways on paper: +
++ Read any of the lines above as: “three times four equals twelve,” or “three + groups of four.” +
+ ++ The division sign is a dot with a line: ÷. It means + split into equal groups or share fairly. +
++ Take twelve shared into four equal piles; each pile has three. Again, the same + fact can look different on the page: +
++ Read 12 ÷ 4 = 3 or 12/4 = 3 as: “twelve divided by four + equals three.” Twelve dots shared into four equal piles give three in each pile. +
++ A slash between two numbers is a quick way to write division or a fraction in one + line: 1/2 is “one half,” and 12/4 is the same sharing story as + twelve divided by four. In typeset math the numbers can sit one above the other: + \(\tfrac{1}{2}\) (one half) and \(\dfrac{12}{4} = 3\) (twelve over four equals three). +
+ ++ The equals sign is two parallel lines: =. It means + is the same amount as on both sides. +
++ Read a full sentence from left to right. In 5 + 2 = 7, the left side (five plus + two) has the same total as the right side (seven). The equals sign is the bridge between them. +
+ +One sentence
++ Treat the whole line as one idea: “five plus two equals seven.” Do not stop reading at the plus + sign — finish at the number after the equals sign. +
++ Round brackets — also called parentheses — wrap part of a + sentence: ( and ). They mean: do this group + first, then use the result with the rest of the line. +
++ In (2 + 3) + 4, add two and three inside the brackets to get five, then add four + to get nine. Without brackets, 2 + 3 + 4 still totals nine, but brackets help + when the order would be unclear. +
+ +| Symbol | +Name | +Meaning | +Example | +
|---|---|---|---|
| + | +plus | +put together | +3 + 4 = 7 | +
| − | +minus | +take away | +7 − 3 = 4 | +
| × | +times | +equal groups | +3 × 4 = 12 | +
| ÷ | +divided by | +fair shares | +12 ÷ 4 = 3 | +
| = | +equals | +same amount both sides | +5 + 2 = 7 | +
| ( ) | +brackets | +this part first | +(2 + 3) + 4 = 9 | +
+ Sometimes we compare two amounts without adding or subtracting. The open mouth of the symbol + points at the bigger number. +
++ You may also see ≤ (less than or equal) and ≥ (greater than or + equal). The extra line means “or the same amount.” +
+ ++ In big numbers like 1,000, a comma groups digits in threes so + the number is easier to read — one thousand, not “one zero zero zero” as separate ideas. +
++ A decimal point . sits between a whole part and a smaller part. + 3.50 might mean three dollars and fifty cents: the part after the point is not + whole dollars. You will learn more about decimals later; for now, remember the dot splits the + number into two pieces. +
+ ++ A fraction names part of a whole split into equal pieces. You + might see a single character like ½, or plain text with a slash + 1/2, or the same value written tall in math as \(\tfrac{1}{2}\) — all mean + one part out of two equal parts. +
++ The percent sign % means out of one hundred. + 50% means fifty out of every hundred — half of the whole. If a test has 100 + points and you score 80, you might say you got 80%. +
+ ++ Three dots in a row … (an ellipsis) mean the pattern keeps + going the same way: 2, 4, 6, 8, … — two, four, six, eight, and so on. +
++ The sign ≈ means approximately or about — close + but not exact. 10 ÷ 3 ≈ 3 is a rough answer; the exact value is a bit more than + three. +
+ ++ As you grow, books will add more symbols: a colon for ratios, small numbers + above the line for powers, and pairs of letters in graphs. You do not need them yet; this chapter + is enough to read everyday number sentences. +
+ ++ Say each line out loud before you calculate. Cover the answer with your hand, then check: +
++ People counted with fingers and words long before they agreed on one way to write math. Ancient + Egyptians and Babylonians used pictures and marks for amounts. Over centuries, different + countries used different symbols for the same ideas. +
++ The equals sign (=) was popularised in the 1500s by Welsh mathematician + Robert Recorde. He chose two lines because “no two things can be more equal” than + parallel lines — a way to show both sides match. +
++ The plus and minus signs (+ and −) became common in Europe + around the same era, replacing longer Latin words. The times sign (×) and + division sign (÷) appeared later, when printing books needed short, clear marks + that fit on one line. +
++ Brackets grew important when formulas got longer — mathematicians needed a visible rule for + “which part first,” just like you do in (2 + 3) + 4. +
+ ++ Writing “three plus four equals seven” every time is long. Symbols are a shorthand: + the same meaning in less space, so you can compare many sentences quickly. +
+ ++ If the left side of \(=\) counts to \(a\) and the right side counts to \(b\), then \(a = b\) + means both sides name the same number. If they were different, the sentence would + be false — like claiming \(3 + 4 = 8\) when seven dots are the true total. +
+ ++ Without a rule, \(2 + 3 \times 4\) could be read in two ways. Brackets fix one group: + \((2 + 3) \times 4 = 5 \times 4 = 20\). Later you will learn more order rules; for now, + brackets always mean “work inside first.” +
+ +Pause and answer in your head or with a partner.
+ +Checkpoint
+What is the name of the sign in \(7 - 3 = 4\)? What does it tell you to do?
+Checkpoint
+Say out loud: \(4 \times 2 = 8\). Which word goes with \(\times\)?
+Checkpoint
+In \((5 + 1) + 2\), which part do you work out first? What is the final total?
+Checkpoint
+Is \(6 > 2\) true? What does the open side of \(>\) point toward?
+Checkpoint
+What does \(50\%\) mean in words (“out of …”)?
+Answer: A cross-shaped mark + that means add or put together.
+Answer: “Five equals five.”
+Answer: Minus: − (or - on a keyboard).
+Answer: “Nine divided by three equals three.”
+Answer: Multiply — four groups of two (or two groups of four), total eight.
+Answer: \(9\).
+Steps: Inside brackets: \(3 + 2 = 5\). Then \(5 + 4 = 9\).
+Answer: True — four is less than nine.
+Answer: Seven is bigger. Examples: \(7 > 5\) or \(5 < 7\).
+Answer: One half — one part out of two equal parts.
+Answer: Twenty-five out of every hundred — a quarter of the price is taken off (you will learn to compute the exact dollars later).
+Answer: \((2 \times 3) + 1 = 7\). \(2 \times (3 + 1) = 2 \times 4 = 8\). They are not the same — brackets change the result.
+Explanation: Brackets show which group to do first; this is why notation matters.
+Answer: Dot \(\cdot\) and asterisk \(*\) (on keyboards/calculators).
+Answer: “One thousand plus five hundred equals one thousand five hundred.” The comma groups digits in threes to show thousands.
+