Question

mastery check: solving proportions

solve for the variable.

1. \\(\frac{2}{t} = \frac{8}{12}\\)

\\(t = \\)

1. \\(\frac{5}{7} = \frac{h}{6}\\)

\\(h = \\)

1. \\(\frac{25}{35} = \frac{10}{k}\\)

\\(k = \\)

1. \\(\frac{13}{2} = \frac{6}{n}\\)

\\(n = \\)

1. \\(\frac{x}{5} = \frac{12}{15}\\)

\\(x = \\)

1. \\(\frac{7}{y} = \frac{11}{4}\\)

\\(y = \\)

1. \\(\frac{9}{4} = \frac{d}{24}\\)

\\(d = \\)

1. \\(\frac{b}{9} = \frac{7}{8}\\)

\\(b = \\)

1. \\(\frac{12}{f} = \frac{42}{28}\\)

\\(f = \\)

challenge:

1. \\(\frac{a}{119} = \frac{13}{91}\\)

\\(a = \\)

1. \\(\frac{63}{10.5} = \frac{j}{2}\\)

\\(j = \\)

Explanation:

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<reasoning>

Solve questions 1 to 3

1. \(\frac{2}{T} = \frac{8}{12} \implies 8T = 24 \implies T = 3\)
2. \(\frac{5}{7} = \frac{H}{6} \implies 7H = 30 \implies H = \frac{30}{7}\)
3. \(\frac{25}{35} = \frac{10}{k} \implies \frac{5}{7} = \frac{10}{k} \implies 5k = 70 \implies k = 14\)

Solve questions 4 to 7

1. \(\frac{13}{2} = \frac{6}{N} \implies 13N = 12 \implies N = \frac{12}{13}\)
2. \(\frac{x}{5} = \frac{12}{15} \implies \frac{x}{5} = \frac{4}{5} \implies x = 4\)
3. \(\frac{7}{y} = \frac{11}{4} \implies 11y = 28 \implies y = \frac{28}{11}\)
4. \(\frac{9}{4} = \frac{d}{24} \implies d = 9 \times 6 \implies d = 54\)

Solve questions 8 to 11

1. \(\frac{b}{9} = \frac{7}{8} \implies 8b = 63 \implies b = \frac{63}{8}\)
2. \(\frac{12}{f} = \frac{42}{28} \implies \frac{12}{f} = \frac{3}{2} \implies 3f = 24 \implies f = 8\)
3. \(\frac{A}{119} = \frac{13}{91} \implies \frac{A}{119} = \frac{1}{7} \implies 7A = 119 \implies A = 17\)
4. \(\frac{63}{10.5} = \frac{j}{2} \implies 6 = \frac{j}{2} \implies j = 12\)

</reasoning>

<answer>

No.	Answer
2	\(H = \frac{30}{7}\) (or \(4\frac{2}{7}\))
3	\(k = 14\)
4	\(N = \frac{12}{13}\)
5	\(x = 4\)
6	\(y = \frac{28}{11}\) (or \(2\frac{6}{11}\))
7	\(d = 54\)
8	\(b = \frac{63}{8}\) (or \(7\frac{7}{8}\))
9	\(f = 8\)
10	\(A = 17\)
11	\(j = 12\)

</answer>

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Answer:

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<reasoning>

Solve questions 1 to 3

1. \(\frac{2}{T} = \frac{8}{12} \implies 8T = 24 \implies T = 3\)
2. \(\frac{5}{7} = \frac{H}{6} \implies 7H = 30 \implies H = \frac{30}{7}\)
3. \(\frac{25}{35} = \frac{10}{k} \implies \frac{5}{7} = \frac{10}{k} \implies 5k = 70 \implies k = 14\)

Solve questions 4 to 7

1. \(\frac{13}{2} = \frac{6}{N} \implies 13N = 12 \implies N = \frac{12}{13}\)
2. \(\frac{x}{5} = \frac{12}{15} \implies \frac{x}{5} = \frac{4}{5} \implies x = 4\)
3. \(\frac{7}{y} = \frac{11}{4} \implies 11y = 28 \implies y = \frac{28}{11}\)
4. \(\frac{9}{4} = \frac{d}{24} \implies d = 9 \times 6 \implies d = 54\)

Solve questions 8 to 11

1. \(\frac{b}{9} = \frac{7}{8} \implies 8b = 63 \implies b = \frac{63}{8}\)
2. \(\frac{12}{f} = \frac{42}{28} \implies \frac{12}{f} = \frac{3}{2} \implies 3f = 24 \implies f = 8\)
3. \(\frac{A}{119} = \frac{13}{91} \implies \frac{A}{119} = \frac{1}{7} \implies 7A = 119 \implies A = 17\)
4. \(\frac{63}{10.5} = \frac{j}{2} \implies 6 = \frac{j}{2} \implies j = 12\)

</reasoning>

<answer>

No.	Answer
2	\(H = \frac{30}{7}\) (or \(4\frac{2}{7}\))
3	\(k = 14\)
4	\(N = \frac{12}{13}\)
5	\(x = 4\)
6	\(y = \frac{28}{11}\) (or \(2\frac{6}{11}\))
7	\(d = 54\)
8	\(b = \frac{63}{8}\) (or \(7\frac{7}{8}\))
9	\(f = 8\)
10	\(A = 17\)
11	\(j = 12\)

</answer>

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