equivalent forms
Simplify the fraction 6/8 to lowest terms.
3/4
What is the greatest common factor (GCF) of 12 and 18? Use it to simplify 12/18.
GCF(12,18)=6; 12/18 = 2/3
Claire ate 2/4 of a pizza. Write this fraction in lowest terms.
2/4 = 1/2.
Place 3/6 on a number line and write its simplified form.
3/6 = 1/2.
Simplify the fraction part of 1 4/8.
1 4/8 → 1 1/2.
Simplify 15/35 to lowest terms.
3/7
ist two strategies you can use to simplify fractions (no more than one sentence each).
Example answers: (1) Divide numerator and denominator by GCF. (2) Use prime factorization to cancel common primes.
A recipe needs 6/9 cup of milk. Simplify the fraction for the recipe.
6/9 = 2/3
Which is closer to 0: 5/10 or 3/8? Simplify any fractions you use to compare.
5/10 = 1/2; 3/8 = 0.375, 1/2 = 0.5, so 3/8 is closer to 0.
Convert 9/6 to a mixed number and then simplify the fractional part.
9/6 = 1 3/6 → simplify 3/6 to 1/2 → 1 1/2.
Are 4/6 and 2/3 equivalent?
Yes. 4/6 = 2/3; lowest terms both 2/3
Simplify 84/98 by using prime factorization. Show steps.
84 = 2^2 * 3 * 7; 98 = 2 * 7^2; cancel 2*7 => GCF=14; 84/98 = 6/7.
Sam ran 9/12 of a mile. Put this in lowest terms and state how much of a mile he ran as a fraction in simplest form
9/12 = 3/4
On a number line from 0 to 1, mark 7/14 and 1/2. Are they the same point? Explain and show simplification.
7/14 = 1/2; same point.
A cake recipe uses 11/4 cups of flour. Write it as a mixed number and simplify any fraction part.
11/4 = 2 3/4 (3/4 already simplified).
Simplify 45/60. Show the GCF you used
15; 45/60 = 3/4.
Explain how you would use division by common factors repeatedly to simplify 48/180. Then give the simplified result.
48/180 divide by 12? GCF(48,180)=12; 48/180 = 4/15.
A ribbon is 56/72 meters long. Simplify to lowest terms and state how much was cut off if originally it was 1 meter (write the remaining length in simplest form).
56/72 simplify GCF=8 => 7/9. Cut off = 1 - 7/9 = 2/9.
A point is at 10/15 on the number line. Simplify the fraction and give the decimal to two places.
10/15 simplify GCF=5 => 2/3 ≈ 0.67.
Convert 29/12 to a mixed number. Then simplify the fractional part and show the steps.
29/12 = 2 5/12 (5/12 simplified).
A student claims 14/28 simplified is 7/14. Is the student correct? If not, give the correct simplification and explain the error
Incorrect. 14/28 = 1/2 (student divided only numerator).
Given the fraction 231/308, find its GCF and simplify to lowest terms. Show your method.
GCF(231,308)=11; 231/308 = 21/28; then GCF(21,28)=7 => 3/4.
A jug is 315/420 full of juice. Simplify this fraction and explain (in one sentence) why simplifying helps compare how full the jug is to another jug that is 3/4 full.
315/420 divide by 105 => 3/4. Simplifying shows it equals 3/4 so they are the same fullness.
Convert 121/143 to lowest terms (if possible). If it is already in lowest terms, explain how you know using number-line or factor reasoning.
121 and 143 share no common prime factors (121=11^2, 143=11*13) — they share 11, so divide: 121/143 = 11/13.
A student wrote 22/16 = 1 6/16 and left the fraction. Correct the mixed-number form and simplify completely, showing GCF steps.
22/16 = 1 6/16 → simplify 6/16 by GCF=2 → 1 3/8.