Skip to content
MeerkatSkool Afrikaans
Summaries · Grade 7 Maths › Converting and comparing fractions
Free summary · Grade 7 Maths

Converting and comparing fractions

Numerator and denominator, comparing, equivalent fractions and adding and subtracting fractions. Tenths, hundredths and the decimal comma; comparing and calculating with decimals. Read one part at a time and tap “I know this”. Then test yourself in the quiz.

Know it already? Jump straight to the quiz

Your progress0 of 7

What is a fraction?

A fraction is part of a whole. The denominator (bottom) says into how many equal parts the whole is cut; the numerator (top) says how many parts we have.

1 whole½²⁄₄½ = ²⁄₄: the same amount
½ = ²⁄₄
Tap when you could tell someone without looking.

Compare, equivalent and simplify

  • Same denominator: bigger numerator = bigger fraction: ⅗ > ⅖.
  • Same numerator: bigger denominator = smaller pieces: ⅓ > ⅕.
  • Equivalent fractions: multiply or divide top and bottom by the same number: ½ = ²⁄₄ = ³⁄₆.
  • Simplify: divide top and bottom by the same factor: ⁶⁄₈ = ¾.
Tap when you could tell someone without looking.

Adding and subtracting

Rule

First make the denominators the same, then add only the numerators: ½ + ¼ = ²⁄₄ + ¼ = ¾.

Watch out

Never add the denominators: ½ + ¼ is not ²⁄₆.

Multiply: top × top, bottom × bottom: ⅔ × ¾ = ⁶⁄₁₂ = ½. Divide: flip the second fraction and multiply: ½ ÷ ¼ = ½ × ⁴⁄₁ = 2.

Subtracting mixed numbers: 2½ − 1⅔ = ⁵⁄₂ − ⁵⁄₃ = ¹⁵⁄₆ − ¹⁰⁄₆ = ⁵⁄₆. Fraction of an amount: ⅗ of 40 = 40 ÷ 5 × 3 = 24.

Tap when you could tell someone without looking.

Grade 7: unlike denominators and multiplying

  • Unlike denominators: find the LCM of the denominators. ⅔ + ¼ = ⁸⁄₁₂ + ³⁄₁₂ = ¹¹⁄₁₂.
  • Mixed number to improper fraction: 2¾ = (2 × 4 + 3)⁄4 = ¹¹⁄₄.
  • Multiply: numerator × numerator and denominator × denominator. ⅔ × ¾ = ⁶⁄₁₂ = ½.
  • With mixed numbers: first make them improper fractions. 1½ × ⅔ = ³⁄₂ × ⅔ = ⁶⁄₆ = 1.
  • Write the answer in its simplest form: divide numerator and denominator by their HCF.
Tap when you could tell someone without looking.

Decimal fractions

The decimal comma separates the whole number from the parts. After the comma: tenths, hundredths, thousandths.

FractionDecimal
½0,5
¼0,25
¾0,75
¹⁄₁₀0,1
³⁄₁₀₀0,03
Watch out

0,5 is bigger than 0,45: compare tenths first (5 tenths vs 4 tenths). More digits after the comma do not make a number bigger.

Place value: in 4,37 the 3 is worth 3 tenths (0,3) and the 7 is worth 7 hundredths (0,07). From small to big: 0,09; 0,35; 0,4; 0,5. Counting in hundredths: 0,97; 0,98; 0,99; 1,00; 1,01.

Tap when you could tell someone without looking.

Calculating with decimals

  • Add and subtract: line up the commas: 3,5 + 1,25 = 4,75.
  • × 10: the comma moves one place right: 3,45 × 10 = 34,5.
  • ÷ 10: the comma moves one place left: 3,45 ÷ 10 = 0,345.
  • × 100: the comma moves two places right: 3,45 × 100 = 345; ÷ 100: two places left: 45 ÷ 100 = 0,45.
  • Multiply 0,3 × 0,2: 3 × 2 = 6; two digits after the comma → 0,06.
Tap when you could tell someone without looking.

Three decimal places

  • Thousandths: 3,147 = 3 + 0,1 + 0,04 + 0,007.
  • Round to 2 decimal places: look at the third digit. 3,147 → 3,15; 6,082 → 6,08.
  • Multiply: 2,345 × 3 = 7,035. 0,4 × 0,3 = 0,12: count the decimal places in the question (1 + 1 = 2): the answer has that many places.
  • Divide by a whole number: 4,326 ÷ 3 = 1,442. Check with rounding or a calculator.
Tap when you could tell someone without looking.

Remember this and test yourself

Remember this: your summary
  • Denominator = number of equal parts; numerator = how many we have.
  • After the comma: tenths, hundredths, thousandths.
  • Bigger denominator = smaller pieces.
  • ½ = 0,5; ¼ = 0,25; ¾ = 0,75.
  • Equivalent: multiply top and bottom by the same number.
  • Compare tenths first, then hundredths.

Write these points in your book. Read them again the night before the test.

Memory trick

The denominator names the kind of piece; the numerator counts how many you have.

Flash cards · Tap to turn over

Important words

First say the answer yourself, then turn the card over.

Test yourself · Part 2

True or false?

Read the question and the answer. Is the answer right? Tap True or False.

    Now the real quiz!

    The quiz has many more questions on this topic. Every question shows straight away whether you are right and explains why.

    Take the quiz: Converting and comparing fractions
    Practise it step by step: Extra Maths ClassAll Grade 7 Maths summaries
    For parents
    • Let your child work the examples on paper and explain them to you.
    • The ticks (“I know this”) are saved on this device only. We never ask for names or emails.

    Follows CAPS for Grade 7 Mathematics. Always check your teacher’s notes and textbook too.

    Free PDF