Question

11
$3\frac{5}{6}$
$+2\frac{13}{15}$

12
$6\frac{2}{15}$
$-\frac{6}{25}$

13
$1\frac{1}{10} \times 2\frac{2}{11} =$

14
$4\frac{1}{2} \div 2\frac{1}{4} =$

15 simplify:
$\frac{225}{300}$

16 compare using >, <, or =:
$3 - 4 \bigcirc 4 - 3$

17 find the greatest common factor:
100, 64

18 find the least common multiple:
17, 34

19 evaluate:
$5^2 + 2(7 - 5) + 3$

20 solve:
$x - (-24) = 30$

Explanation:

Step1: Add whole numbers first

$3 + 2 = 5$

Step2: Find common denominator for fractions

Least common denominator of 6 and 15 is 30.
$\frac{5}{6} = \frac{25}{30}$, $\frac{13}{15} = \frac{26}{30}$

Step3: Add the fractions

$\frac{25}{30} + \frac{26}{30} = \frac{51}{30} = 1\frac{21}{30} = 1\frac{7}{10}$

Step4: Add to whole number sum

$5 + 1\frac{7}{10} = 6\frac{7}{10}$

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Step1: Convert mixed number to fraction

$6\frac{2}{15} = \frac{92}{15}$

Step2: Find common denominator

Least common denominator of 15 and 25 is 75.
$\frac{92}{15} = \frac{460}{75}$, $\frac{6}{25} = \frac{18}{75}$

Step3: Subtract the fractions

$\frac{460}{75} - \frac{18}{75} = \frac{442}{75} = 5\frac{67}{75}$

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Step1: Convert mixed numbers to improper fractions

$1\frac{1}{10} = \frac{11}{10}$, $2\frac{2}{11} = \frac{24}{11}$

Step2: Multiply the fractions

$\frac{11}{10} \times \frac{24}{11} = \frac{24}{10} = \frac{12}{5} = 2\frac{2}{5}$

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Step1: Convert mixed numbers to improper fractions

$4\frac{1}{2} = \frac{9}{2}$, $2\frac{1}{4} = \frac{9}{4}$

Step2: Rewrite division as multiplication

$\frac{9}{2} \div \frac{9}{4} = \frac{9}{2} \times \frac{4}{9}$

Step3: Simplify and calculate

$\frac{9 \times 4}{2 \times 9} = \frac{4}{2} = 2$

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Step1: Find GCD of numerator and denominator

Greatest common divisor of 225 and 300 is 75.

Step2: Divide by GCD

$\frac{225 \div 75}{300 \div 75} = \frac{3}{4}$

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Step1: Calculate both expressions

$3 - 4 = -1$, $4 - 3 = 1$

Step2: Compare the results

$-1 < 1$

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Step1: List factors of each number

Factors of 100: $1, 2, 4, 5, 10, 20, 25, 50, 100$
Factors of 64: $1, 2, 4, 8, 16, 32, 64$

Step2: Identify largest common factor

Greatest common factor is 4

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Step1: List multiples of each number

Multiples of 17: $17, 34, 51, ...$
Multiples of 34: $34, 68, 102, ...$

Step2: Identify smallest common multiple

Least common multiple is 34

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Step1: Evaluate exponent and parentheses

$5^2 = 25$, $7 - 5 = 2$

Step2: Perform multiplication

$2 \times 2 = 4$

Step3: Add all terms

$25 + 4 + 3 = 32$

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Step1: Simplify the left side

$x - (-24) = x + 24$

Step2: Solve for x

$x + 24 = 30$
$x = 30 - 24 = 6$

Answer:

1. $6\frac{7}{10}$
2. $5\frac{67}{75}$
3. $2\frac{2}{5}$
4. $2$
5. $\frac{3}{4}$
6. $3-4 < 4-3$
7. $4$
8. $34$
9. $32$
10. $x=6$