Problem Set 17 – Equivalent FractionsClass 5 Maths · Chapter 5 Fractions · Problem Set 17 – Maharashtra Board

Summary: Problem Set 17 – Equivalent Fractions

In 3/5, the top number 3 is the numerator and the bottom number 5 is the denominator.

Fractions that show the same amount are called equivalent fractions: 1/2 = 2/4 = 3/6.

Multiply the numerator and the denominator by the same number (not 0) to get an equivalent fraction: 2/5 = 6/15.

If the numerator and denominator have a common divisor, divide both by it to get an equivalent fraction: 6/15 = 2/5.

To fill a box like 5/8 = ?/24, ask 'how many times 8 makes 24?' and multiply the numerator by the same number.

Key points to remember

• Numerator on top, denominator below
• Equivalent fractions have the same value
• 1/2 = 2/4 = 3/6 = 4/8
• Multiply top and bottom by the same non-zero number
• Divide top and bottom by a common divisor
• Whatever you do to the bottom, do to the top
• 5/8 = 15/24 (both × 3)
• 20/36 = 5/9 (both ÷ 4)

Problem Set 17 – Equivalent Fractions – Notes

1. Same amount, different names

• Cut a chapati into 2 equal parts and take 1: that is 1/2.
• Cut the same size chapati into 4 equal parts and take 2: that is 2/4 — the same amount.
• So 1/2 and 2/4 are equivalent fractions. We write 1/2 = 2/4.

2. Making equivalent fractions by multiplying

• Cut every piece into more equal pieces: the number of shaded pieces and the number of all pieces both grow by the same times.
• 2/3 = (2 × 2)/(3 × 2) = 4/6 and 2/3 = (2 × 5)/(3 × 5) = 10/15.
• Never multiply by 0 — that does not make a fraction.

3. Making equivalent fractions by dividing

• If the numerator and denominator can both be divided by the same number, divide them.
• 20/36: both divide by 4 → 5/9. Both also divide by 2 → 10/18.
• So 20/36 = 10/18 = 5/9 — all are equivalent.

4. Filling the box

• 3/4 = ?/20: 4 × 5 = 20, so ? = 3 × 5 = 15.
• 18/24 = 3/?: 18 ÷ 6 = 3, so ? = 24 ÷ 6 = 4.
• Find the 'times' or 'divide by' number from the pair you know, then use it on the other.

5. Checking if two fractions are equivalent

• Bring both to the same denominator, or divide each down to its simplest form.
• 4/10 and 6/15: 4/10 = 2/5 and 6/15 = 2/5, so they are equivalent.
• 2/6 and 3/8: 2/6 = 1/3 but 3/8 cannot be made into 1/3, so they are not equivalent.

Formulas at a glance

Key terms

Problem Set 17 – Equivalent Fractions – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 17 – Equivalent Fractions – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 17 – Equivalent Fractions

⏱ About 25 minutes

1. See it (5 min)
   Fold a paper strip into 2, then 4, then 8 parts and see that 1/2 = 2/4 = 4/8.
2. Practise (15 min)
   Do the worked example and the 4 'Try it yourself' sums.
3. Review (5 min)
   Go through the flashcards, take the quiz and play 🎮 Play.