Equivalent Fractions
Show two different fraction names for the same shaded area: one using twelfths and one using sixths (use area or length thinking). Write both fractions.
4/12 = 2/6
On a number line from 0 to 1, mark and label 1/2 and 2/4. Are they the same point? Explain briefly.
Yes; they are the same point on a number line.
Which is larger: 1/4 or 1/2? Use benchmark fractions (0, 1/2, 1) to explain.
1/4 < 1/2
(1/4 is less than 1/2)
Which is larger: 3/8 or 3/4. Explain using the idea of same numerator.
3/8 < 3/4
(3/8 is less than 3/4)
A pizza is cut into 8 equal slices. Mia eats 2 slices. Write the fraction of pizza Mia ate and name a fraction equivalent to it with denominator 4.
Mia ate 2/8, which is equal to 1/4.
Draw or describe a fraction equal to 2/3 using twelfths. Explain why they are equal by comparing unit sizes.
2/3 = 8/12
A circle is split into 12 equal pieces; 4 pieces are shaded. On a 6-piece circle, how many pieces would be shaded to show the same amount? Explain by area reasoning.
4/12 = 2/6 ... so, 2 pieces are shaded on a 6-piece circle.
Decide if 5/6 is greater than, equal to, or less than 1/2. Explain by reasoning about size and the benchmark 1/2.
5/6 > 1/2
(5/6 is greater than 1/2)
Which is larger: 4/9 or 4/6? Use reasoning about size of each part.
4/9 < 4/6
(4/9 is less than 4/6)
A recipe calls for 3/4 cup of milk. If you only want half the recipe, how much milk do you need? Explain using area or length models (think of dividing the cup).
Half of 3/4 is 3/8
Find two different fractions equal to 4/5, using denominators 10 and 100. Explain with a length model (number of equal parts and part size).
4/5 = 8/10 = 40/100
Show on a number line how 3/8 and 9/24 represent the same point. Describe the unit lengths used in each fraction.
3/8 = 9/24 ... you should have a drawing showing the equal pieces with the correct amount shaded
Compare 7/10 and 3/4. Use area or length models (or both) to justify which is larger and write the comparison using >, <, or =.
7/10 < 3/4
(7/10 is less than 3/4) ... can compare on a number line or draw a visual model
Compare 5/12 and 3/12. Explain quickly and record the symbol.
5/12 > 3/12
(5/12 is greater than 3/12)
A water bottle is filled to 6/10 of its capacity. Give an equivalent fraction with denominator 5 and explain why it is the same amount.
6/10 is equal to 3/5
Given a rectangle divided into 8 equal strips with 3 shaded, write an equivalent fraction with denominator 24 and explain how the parts changed but the amount stayed the same.
3/8 = 9/24
A ribbon is 1 whole. You cut it into 5 equal parts and shade 2. Now, cut the same ribbon into 10 equal parts. How many parts would you shade to show the same amount? Explain using length model language.
You would shade 4 parts out of 10 ... 2/5 = 4/10
Determine whether 5/12 is more or less than 1/2. Explain using reasoning about halves and partition sizes.
5/12 < 1/2
(5/12 is less than 1/2) ... because half of 12 is 6, and 5 is less than 6
Which is larger: 7/10 or 7/12? Explain using the fact that denominators tell part size.
7/10 > 7/12
(7/10 is greater than 7/12)
A class reads 9/12 of a book. Express this amount in a simpler equivalent fraction and explain using an area model or partitioning the pages.
9/12 is equal to 3/4
Explain why 6/10 is equivalent to 3/5 using both an area model (a partitioned square) and a length model (number line). Be explicit about how the number and size of parts differ.
6/10 = 3/5
Draw a rectangle divided into 4 equal rows and then into 6 equal columns (making 24 small equal rectangles). Shade 6 of them. Give two fraction names for the shaded part and explain why they represent the same amount.
6/24 = 1/4 ... OR ... 6/24 = 3/12
(depends on what model you chose to draw)
Compare 11/12 and 5/6. Use benchmark reasoning and/or area models to justify your answer and write the correct symbol.
11/12 > 5/6 , since 5/6 = 10/12
(11/12 is greater than 5/6, since 5/6 is equal to 10/12)
Put these in order from smallest to largest and explain your reasoning: 2/5, 2/3, 2/10. Use common numerator reasoning and benchmark help.
From smallest to largest: 2/10, 2/5, 2/3
You run a track that is 1 whole lap. If you run 3/4 of a lap and your friend runs 5/8 of a lap, who ran farther? Justify using a length model (number line) and write the comparison using >, <, or =.
3/4 > 5/8
(3/4 is greater than 5/8)