Question

lets practice!! solve each equation. check your solution.
\\(\frac{1}{7}t = 3\\)
\\(\frac{4}{5}t = 8\\)
\\(\frac{1}{9}t = 6\\)
\\(\frac{3}{5}t = 6\\)
\\(\frac{2}{3} = \frac{3}{10}t\\)
\\(\frac{1}{4}a = \frac{4}{15}\\)
\\(\frac{a}{9} = 11\\)
\\(\frac{h}{8} = 6\\)

Explanation:

Equation 1: $\frac{1}{7}t=3$

Step1: Multiply by 7

$t=3\times7$

Step2: Calculate product

$t=21$

Check:

Substitute $t=21$ into original equation: $\frac{1}{7}\times21=3$, which is true.

Equation 2: $\frac{1}{9}t=6$

Step1: Multiply by 9

$t=6\times9$

Step2: Calculate product

$t=54$

Check:

Substitute $t=54$ into original equation: $\frac{1}{9}\times54=6$, which is true.

Equation 3: $\frac{2}{3}=\frac{3}{10}t$

Step1: Multiply by $\frac{10}{3}$

$t=\frac{2}{3}\times\frac{10}{3}$

Step2: Calculate product

$t=\frac{20}{9}$

Check:

Substitute $t=\frac{20}{9}$ into original equation: $\frac{3}{10}\times\frac{20}{9}=\frac{60}{90}=\frac{2}{3}$, which is true.

Equation 4: $\frac{a}{9}=11$

Step1: Multiply by 9

$a=11\times9$

Step2: Calculate product

$a=99$

Check:

Substitute $a=99$ into original equation: $\frac{99}{9}=11$, which is true.

Equation 5: $\frac{4}{5}t=8$

Step1: Multiply by $\frac{5}{4}$

$t=8\times\frac{5}{4}$

Step2: Calculate product

$t=10$

Check:

Substitute $t=10$ into original equation: $\frac{4}{5}\times10=8$, which is true.

Equation 6: $\frac{3}{5}t=6$

Step1: Multiply by $\frac{5}{3}$

$t=6\times\frac{5}{3}$

Step2: Calculate product

$t=10$

Check:

Substitute $t=10$ into original equation: $\frac{3}{5}\times10=6$, which is true.

Equation 7: $\frac{1}{4}a=\frac{4}{15}$

Step1: Multiply by 4

$a=\frac{4}{15}\times4$

Step2: Calculate product

$a=\frac{16}{15}$

Check:

Substitute $a=\frac{16}{15}$ into original equation: $\frac{1}{4}\times\frac{16}{15}=\frac{16}{60}=\frac{4}{15}$, which is true.

Equation 8: $\frac{h}{8}=6$

Step1: Multiply by 8

$h=6\times8$

Step2: Calculate product

$h=48$

Check:

Substitute $h=48$ into original equation: $\frac{48}{8}=6$, which is true.

Answer:

1. $t=21$
2. $t=54$
3. $t=\frac{20}{9}$
4. $a=99$
5. $t=10$
6. $t=10$
7. $a=\frac{16}{15}$
8. $h=48$