Why two fractions can be equal: the same whole cut into more, smaller pieces. Your child uses pictures, then multiplies or divides the top and bottom by the same number.
Cut each piece into 3 and there are 3 times as many pieces, and 3 times as many shaded: 1/2 = 3/6. Multiply or divide the top and bottom by the same number.
equivalentworth the same amount
numeratorthe top number: how many parts
denominatorthe bottom number: parts in the whole
simplest formfewest pieces, like 1/2 for 4/8
Watch for: Multiplying only the top or only the bottom. Adding the same number to the top and bottom: 1/2 is not 2/3. Counting the shaded pieces before the new cuts instead of after.
At home: Cut a sandwich in half, then cut each half into 2 or 3. Count the pieces to see 1/2 = 2/4 = 3/6.
Sample sheet and answer key
Luna's Space Adventure
Grade 4 · Equivalent fractions · 4.NF.A.1
NameDate
Astronaut Luna is exploring a far-off corner of space. Solve each problem to help Luna's mission go smoothly!
Cut the pieces smaller
The same amount, cut into more pieces. Write both fractions.
Multiply top and bottom
Multiply the numerator and denominator by the same number.
35=45=25=45=23=36=
Go the other way
Divide top and bottom by the same number.
24=39=36=
Sheet
Luna's Space Adventure
Grade 4 · Equivalent fractions · 4.NF.A.1
Answer key
Astronaut Luna is exploring a far-off corner of space. Solve each problem to help Luna's mission go smoothly!
Cut the pieces smaller
The same amount, cut into more pieces. Write both fractions.
12
36
24
612
Multiply top and bottom
Multiply the numerator and denominator by the same number.
35=61045=121525=82045=162023=101536=1224
Go the other way
Divide top and bottom by the same number.
24=1239=1336=12
Answer key
New problems every time, three levels (gentle, core and stretch), themes to pick from, a second page if you want one. Each sheet comes with an answer key and a one-page guide for grown-ups.