Question

① (1\frac{3}{4}+3\frac{5}{16}+\frac{5}{9}) ② betsy needed some fabric to make flags. she bought (4\frac{1}{8}) yd of red fabric, (4\frac{2}{3}) yd of white fabric, and (3\frac{1}{4}) yd of blue fabric. about how much fabric did she buy altogether? __ yd ③ diane went salmon fishing with her father. diane caught a fish that weighed (16\frac{3}{8}) lb. her father caught one that weighed (10\frac{1}{16}) lb. about how much heavier was dianes fish? __ lb

Explanation:

Step1: Convert mixed - numbers to improper fractions for E

$4\frac{1}{8}=\frac{4\times8 + 1}{8}=\frac{33}{8}$, $4\frac{2}{3}=\frac{4\times3+2}{3}=\frac{14}{3}$, $3\frac{1}{4}=\frac{3\times4 + 1}{4}=\frac{13}{4}$

Step2: Find a common denominator for E

The common denominator of 8, 3 and 4 is 24. $\frac{33}{8}=\frac{33\times3}{8\times3}=\frac{99}{24}$, $\frac{14}{3}=\frac{14\times8}{3\times8}=\frac{112}{24}$, $\frac{13}{4}=\frac{13\times6}{4\times6}=\frac{78}{24}$

Step3: Add the fractions for E

$\frac{99}{24}+\frac{112}{24}+\frac{78}{24}=\frac{99 + 112+78}{24}=\frac{289}{24}=12\frac{11}{24}$

Step4: Convert mixed - numbers to improper fractions for D

$16\frac{3}{8}=\frac{16\times8+3}{8}=\frac{131}{8}$, $10\frac{1}{16}=\frac{10\times16 + 1}{16}=\frac{161}{16}$

Step5: Find a common denominator for D

The common denominator of 8 and 16 is 16. $\frac{131}{8}=\frac{131\times2}{8\times2}=\frac{262}{16}$

Step6: Subtract the fractions for D

$\frac{262}{16}-\frac{161}{16}=\frac{262 - 161}{16}=\frac{101}{16}=6\frac{5}{16}$

Answer:

E. $12\frac{11}{24}$; D. $6\frac{5}{16}$