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Simplifying Fractions Using HCF
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Simplifying Fractions Using HCF
Ari and Freya are checking fractions on supply labels at the fire station. Simplify each fraction by dividing its numerator and denominator by their highest common factor (HCF). Give answers in simplest form.
Find the HCF
Use common factors to identify the greatest shared factor.
1.Ari lists the factors of 28 and 42. Write the HCF of 28 and 42, and show one pair of common factors that helped you decide.
2.Freya needs the HCF of 36 and 54 to simplify a label. What is the HCF? Include a brief method, such as listing factors or using prime factors.
3.Which pair of numbers has an HCF of 9? Choose one answer.
- 18 and 27
- 24 and 36
- 21 and 35
- 16 and 40
Simplify the supply labels
Divide both parts of each fraction by the same HCF. Check that no common factor greater than 1 remains.
4.A supply box is marked 30/45 full. Find the HCF of 30 and 45, then simplify 30/45. Show the division you use.
5.Simplify 42/56 using the HCF. Write the HCF and the simplified fraction.
6.Oliver simplifies 24/60 by dividing the numerator and denominator by 6 and gets 4/10. Is his answer in simplest form? If not, finish simplifying it.
7.Select every fraction that is already in simplest form.
- 5/12
- 8/14
- 9/25
- 15/21
8.A label shows 63/81 of a water tank's capacity. Simplify the fraction using its HCF. Explain how you know your result is fully simplified.
9.Ari says 32/48 simplifies to 2/3 because he divided both numbers by 16. Freya says it simplifies to 3/4. Who is correct? Explain what went wrong, if anything.
10.Challenge: A fraction has numerator 84 and simplifies to 7/11. Find its denominator and state the HCF used to simplify it.
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