rewrite fractions with
a common denominator
1 (ap) reason luis reads about two popular cell phone
apps. one app uses $\frac{1}{2}$ of a phones storage space. the
other app uses $\frac{5}{12}$ of a phones storage space. explain
how luis can find the difference in the storage space
of the two apps without drawing a visual model.

use a common denominator to write equivalent fractions.
2 $\frac{1}{4}$, $\frac{2}{3}$
3 $\frac{11}{12}$, $\frac{1}{4}$
4 $\frac{1}{3}$, $\frac{4}{5}$
5 $\frac{3}{5}$, $\frac{1}{3}$
6 $\frac{5}{6}$, $\frac{1}{12}$
7 $\frac{7}{8}$, $\frac{2}{3}$

8 math on the spot arnold had three pieces of different color
string all the same length. arnold cut the blue string into
2 equal-sized lengths. he cut the red string into 5 equal-sized
lengths, and the green string into 10 equal-sized lengths. he
needs to cut the string so each color has the same number of
equal-sized lengths. what is the least number of equal-sized
lengths each color string could have?

Question

rewrite fractions with
a common denominator
1 (ap) reason luis reads about two popular cell phone
apps. one app uses $\frac{1}{2}$ of a phones storage space. the
other app uses $\frac{5}{12}$ of a phones storage space. explain
how luis can find the difference in the storage space
of the two apps without drawing a visual model.

use a common denominator to write equivalent fractions.
2 $\frac{1}{4}$, $\frac{2}{3}$
3 $\frac{11}{12}$, $\frac{1}{4}$
4 $\frac{1}{3}$, $\frac{4}{5}$
5 $\frac{3}{5}$, $\frac{1}{3}$
6 $\frac{5}{6}$, $\frac{1}{12}$
7 $\frac{7}{8}$, $\frac{2}{3}$

8 math on the spot arnold had three pieces of different color
string all the same length. arnold cut the blue string into
2 equal-sized lengths. he cut the red string into 5 equal-sized
lengths, and the green string into 10 equal-sized lengths. he
needs to cut the string so each color has the same number of
equal-sized lengths. what is the least number of equal-sized
lengths each color string could have?

Accepted Answer

### Problem 2: $\boldsymbol{\frac{1}{4}, \frac{2}{3}}$
# Explanation:
## Step1: Find the least common denominator (LCD) of 4 and 3. The LCD of 4 and 3 is 12 (since 4×3 = 12 and they have no common factors other than 1).
## Step2: Rewrite $\frac{1}{4}$ with denominator 12. Multiply numerator and denominator by 3: $\frac{1	imes3}{4	imes3} = \frac{3}{12}$.
## Step3: Rewrite $\frac{2}{3}$ with denominator 12. Multiply numerator and denominator by 4: $\frac{2	imes4}{3	imes4} = \frac{8}{12}$.
# Answer: $\frac{3}{12}, \frac{8}{12}$

### Problem 3: $\boldsymbol{\frac{11}{12}, \frac{1}{4}}$
# Explanation:
## Step1: Find the LCD of 12 and 4. The LCD is 12 (since 12 is a multiple of 4).
## Step2: $\frac{11}{12}$ already has denominator 12, so it remains $\frac{11}{12}$.
## Step3: Rewrite $\frac{1}{4}$ with denominator 12. Multiply numerator and denominator by 3: $\frac{1	imes3}{4	imes3} = \frac{3}{12}$.
# Answer: $\frac{11}{12}, \frac{3}{12}$

### Problem 4: $\boldsymbol{\frac{1}{3}, \frac{4}{5}}$
# Explanation:
## Step1: Find the LCD of 3 and 5. The LCD is 15 (3×5 = 15, no common factors).
## Step2: Rewrite $\frac{1}{3}$ with denominator 15. Multiply numerator and denominator by 5: $\frac{1	imes5}{3	imes5} = \frac{5}{15}$.
## Step3: Rewrite $\frac{4}{5}$ with denominator 15. Multiply numerator and denominator by 3: $\frac{4	imes3}{5	imes3} = \frac{12}{15}$.
# Answer: $\frac{5}{15}, \frac{12}{15}$

### Problem 5: $\boldsymbol{\frac{3}{5}, \frac{1}{3}}$
# Explanation:
## Step1: Find the LCD of 5 and 3. The LCD is 15 (5×3 = 15).
## Step2: Rewrite $\frac{3}{5}$ with denominator 15. Multiply numerator and denominator by 3: $\frac{3	imes3}{5	imes3} = \frac{9}{15}$.
## Step3: Rewrite $\frac{1}{3}$ with denominator 15. Multiply numerator and denominator by 5: $\frac{1	imes5}{3	imes5} = \frac{5}{15}$.
# Answer: $\frac{9}{15}, \frac{5}{15}$

### Problem 6: $\boldsymbol{\frac{5}{6}, \frac{1}{12}}$
# Explanation:
## Step1: Find the LCD of 6 and 12. The LCD is 12 (12 is a multiple of 6).
## Step2: Rewrite $\frac{5}{6}$ with denominator 12. Multiply numerator and denominator by 2: $\frac{5	imes2}{6	imes2} = \frac{10}{12}$.
## Step3: $\frac{1}{12}$ already has denominator 12, so it remains $\frac{1}{12}$.
# Answer: $\frac{10}{12}, \frac{1}{12}$

### Problem 7: $\boldsymbol{\frac{7}{8}, \frac{2}{3}}$
# Explanation:
## Step1: Find the LCD of 8 and 3. The LCD is 24 (8×3 = 24, no common factors).
## Step2: Rewrite $\frac{7}{8}$ with denominator 24. Multiply numerator and denominator by 3: $\frac{7	imes3}{8	imes3} = \frac{21}{24}$.
## Step3: Rewrite $\frac{2}{3}$ with denominator 24. Multiply numerator and denominator by 8: $\frac{2	imes8}{3	imes8} = \frac{16}{24}$.
# Answer: $\frac{21}{24}, \frac{16}{24}$

### Problem 8: Arnold's Strings
# Explanation:
## Step1: We need to find the least common multiple (LCM) of 2, 5, and 10 (the number of pieces each string is cut into) to find the least number of equal - sized lengths each string could have.
## Step2: Prime factorize the numbers:
 - 2 is prime, so $2 = 2^1$.
 - 5 is prime, so $5 = 5^1$.
 - 10 = 2×5.
## Step3: The LCM is found by taking the highest power of each prime factor. For prime 2, the highest power is $2^1$; for prime 5, the highest power is $5^1$. Then LCM = 2×5 = 10.
# Answer: 10

### Problem 1: Luis's Apps
# Explanation:
## Step1: To find the difference in storage space, we first need a common denominator for $\frac{1}{2}$ and $\frac{5}{12}$. The least common denominator of 2 and 12 is 12.
## Step2: Rewrite $\frac{1}{2}$ with denominator 12. Multiply numerator and denominator by 6: $\frac{1	imes6}{2	imes6}=\frac{6}{12}$.
## Step3: Now that both fractions have the same denominator, we can find the difference by subtracting the numerators: $\frac{6}{12}-\frac{5}{12}=\frac{6 - 5}{12}=\frac{1}{12}$. So Luis can rewrite the fractions with a common denominator (12) and then subtract the numerators.
# Answer: Luis can find a common denominator (12) for $\frac{1}{2}$ (rewritten as $\frac{6}{12}$) and $\frac{5}{12}$, then subtract: $\frac{6}{12}-\frac{5}{12}=\frac{1}{12}$.

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Question

Explanation:

Problem 2: $\boldsymbol{\frac{1}{4}, \frac{2}{3}}$

Step1: Find the least common denominator (LCD) of 4 and 3. The LCD of 4 and 3 is 12 (since 4×3 = 12 and they have no common factors other than 1).

Step2: Rewrite $\frac{1}{4}$ with denominator 12. Multiply numerator and denominator by 3: $\frac{1\times3}{4\times3} = \frac{3}{12}$.

Step3: Rewrite $\frac{2}{3}$ with denominator 12. Multiply numerator and denominator by 4: $\frac{2\times4}{3\times4} = \frac{8}{12}$.

Step1: Find the LCD of 12 and 4. The LCD is 12 (since 12 is a multiple of 4).

Step2: $\frac{11}{12}$ already has denominator 12, so it remains $\frac{11}{12}$.

Step3: Rewrite $\frac{1}{4}$ with denominator 12. Multiply numerator and denominator by 3: $\frac{1\times3}{4\times3} = \frac{3}{12}$.

Step1: Find the LCD of 3 and 5. The LCD is 15 (3×5 = 15, no common factors).

Step2: Rewrite $\frac{1}{3}$ with denominator 15. Multiply numerator and denominator by 5: $\frac{1\times5}{3\times5} = \frac{5}{15}$.

Step3: Rewrite $\frac{4}{5}$ with denominator 15. Multiply numerator and denominator by 3: $\frac{4\times3}{5\times3} = \frac{12}{15}$.

Answer:

Problem 3: $\boldsymbol{\frac{11}{12}, \frac{1}{4}}$