Math Lab
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Equivalent Fractions

Fractions · Class VI

Pick a fraction p/q and a multiplier k. See an equivalent fraction (kp)/(kq).

2
type a value
112
3
type a value
112
4
type a value
110
Live values
  • Original0.6667
  • Scaled numerator8
  • Scaled denominator12
  • Equivalent value0.6667
Live readout
Original0.6667
Scaled numerator8
Scaled denominator12
Equivalent value0.6667
Numerator p2
Denominator q3
Multiplier k4

Formulas in this lab

  • Original
    pq\dfrac{p}{q}
  • Scaled numerator
    k pk\,p
  • Scaled denominator
    k qk\,q
  • Equivalent value
    kpkq\dfrac{kp}{kq}
Tip: Multiplying top and bottom by the same number gives an equivalent fraction.

Frequently asked questions

▶What are equivalent fractions?

Two fractions are equivalent if they represent the same value. Multiplying both numerator and denominator by the same number k gives an equivalent fraction. So 2/3 and 8/12 are equivalent because 8/12 = (4*2)/(4*3).

▶How do I use the equivalent fractions lab?

Pick p, q and k with the sliders. The lab shows p/q and the equivalent (k*p)/(k*q) side by side as decimals. Both should show the same value, even though the numerator and denominator look bigger.

▶How are equivalent fractions used in Indian cooking?

Recipes often scale up or down. If a chai recipe needs 1/2 cup milk per cup of water and you want to make 4 cups of chai, you scale 1/2 to 4/8 by multiplying both parts by 4. Equivalent fractions keep the taste the same.

▶Equivalent fractions vs simplest form: what is the link?

An equivalent fraction can be bigger or smaller in numbers but holds the same value, while simplest form is the smallest pair with GCD 1. So 4/6, 6/9 and 2/3 are all equivalent; only 2/3 is in simplest form. Use the lab to multiply, then divide by GCD to simplify.