Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths
You already know 2/3 and 4/6 name the same amount. Here's why: if you cut every part of a fraction into the same number of smaller pieces, the shaded amount doesn't change, only the number of pieces does. Multiply the numerator and the denominator by the same number, and you get an equivalent fraction.
Priya wants a fraction equivalent to 3/5. She multiplies the numerator and denominator by 2: 3 x 2 = 6, and 5 x 2 = 10. So 3/5 = 6/10.
Names go down as well as up. Priya has another bed of 12 squares with 8 of them planted: 8/12. She groups the 12 squares into 3 blocks of 4, and 2 whole blocks are planted. That is 2/3, the same planting with a smaller name. Divide the numerator and the denominator by the same number and the amount stays put.
Which is more, 3/5 or 5/10? The 5 on top looks bigger than the 3, but fifths and tenths are different sizes, so the top numbers alone cannot settle it. Give both the same bottom number first: 3/5 = 6/10. Now every piece is a tenth, so compare the tops. 6 tenths is more than 5 tenths, so 3/5 is more.
Whatever you do to the numerator, do to the denominator: multiply both by the same number, or divide both by the same number. Change only one of them and the value of the fraction changes.
Multiply or divide the numerator and denominator by the same number, and the fraction's value stays exactly the same. Two fractions with different bottom numbers are easiest to compare once you scale one of them to match the other.
Reading summaries adapted from OpenStax Elementary Algebra (CC BY 4.0), openstax.org.
Last summer you and Mia settled it on the long bed: cut every part into the same number of pieces and the planting does not move, so 2/4 of the bed is 1/2 of the bed. This year the long bed is ruled into 5 strips and 3 of them are planted with onions.
Leo pushes a marker into the middle of every strip, so each strip becomes two thinner ones. How many strips are planted now?
Jobs that lean on this skill. Follow one to see everything it is built on.
14 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.