Numbers and Operations - SSAT Middle Level Quantitative

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Question

$\frac{12}{19}+\frac{7}{19}=$

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Answer

Add the numerators and keep the denominator the same. Then, simplify:

$\frac{12}{19}+\frac{7}{19}=\frac{19}{19}=1$

Answer:

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Question

What is in expanded form?

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Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$5\times10=50$

is in the ones place, so we multiply by .

$3\times1=3$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$2\times\frac{1}{10}=.2$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$6\times\frac{1}{100}=.06$

Then we add the products together.

$\frac{\begin{array}[b]{r}50.00\3.00\ +\ .20\ .06 \end{array}}{ \ \ \space53.26}$

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Question

$\frac{22}{29}+\frac{36}{29}=$

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Answer

Add the numerators and keep the denominator the same. Then, reduce:

$\frac{22}{29}+\frac{36}{29}=\frac{58}{29}=2$

Answer:

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Question

What is in expanded form?

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Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$6\times10=60$

is in the ones place, so we multiply by .

$9\times1=9$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$6\times\frac{1}{10}=.6$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$2\times\frac{1}{100}=.02$

Then we add the products together.

$\frac{\begin{array}[b]{r}60.00\9.00\ +\ .60\ .02 \end{array}}{ \ \ \space69.62}$

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Question

What is in expanded form?

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Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$7\times10=70$

is in the ones place, so we multiply by .

$9\times1=9$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$1\times\frac{1}{10}=.1$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$4\times\frac{1}{100}=.04$

Then we add the products together.

$\frac{\begin{array}[b]{r}70.00\9.00\ +\ .10\ .04 \end{array}}{ \ \ \space79.14}$

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Question

What is in expanded form?

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Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$8\times10=80$

is in the ones place, so we multiply by .

$7\times1=7$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$5\times\frac{1}{10}=.5$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$3\times\frac{1}{100}=.03$

Then we add the products together.

$\frac{\begin{array}[b]{r}80.00\7.00\ +\ .50\ .03 \end{array}}{ \ \ \space87.53}$

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Question

What is in expanded form?

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Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$9\times10=90$

is in the ones place, so we multiply by .

$4\times1=4$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$2\times\frac{1}{10}=.2$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$5\times\frac{1}{100}=.05$

Then we add the products together.

$\frac{\begin{array}[b]{r}90.00\4.00\ +\ .20\ .05 \end{array}}{ \ \ \space94.25}$

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Question

What is in expanded form?

Tap to reveal answer

Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$2\times10=20$

is in the ones place, so we multiply by .

$3\times1=3$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$6\times\frac{1}{10}=.6$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$5\times\frac{1}{100}=.05$

Then we add the products together.

$\frac{\begin{array}[b]{r}20.00\3.00\ +\ .60\ .05 \end{array}}{ \ \ \space23.65}$

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Question

What is in expanded form?

Tap to reveal answer

Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$1\times10=10$

is in the ones place, so we multiply by .

$4\times1=4$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$5\times\frac{1}{10}=.5$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$7\times\frac{1}{100}=.07$

Then we add the products together.

$\frac{\begin{array}[b]{r}10.00\4.00\ +\ .50\ .07 \end{array}}{ \ \ \space14.57}$

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Question

What is in expanded form?

Tap to reveal answer

Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$7\times10=70$

is in the ones place, so we multiply by .

$2\times1=2$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$4\times\frac{1}{10}=.4$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$5\times\frac{1}{100}=.05$

Then we add the products together.

$\frac{\begin{array}[b]{r}70.00\2.00\ +\ .40\ .05 \end{array}}{ \ \ \space72.45}$

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Question

What is in expanded form?

Tap to reveal answer

Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$1\times10=10$

is in the ones place, so we multiply by .

$9\times1=9$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$2\times\frac{1}{10}=.2$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$5\times\frac{1}{100}=.05$

Then we add the products together.

$\frac{\begin{array}[b]{r}10.00\9.00\ +\ .20\ .05 \end{array}}{ \ \ \space19.25}$

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Question

What is in expanded form?

Tap to reveal answer

Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$5\times10=50$

is in the ones place, so we multiply by .

$3\times1=3$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$2\times\frac{1}{10}=.2$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$6\times\frac{1}{100}=.06$

Then we add the products together.

$\frac{\begin{array}[b]{r}50.00\3.00\ +\ .20\ .06 \end{array}}{ \ \ \space53.26}$

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Question

What is in expanded form?

Tap to reveal answer

Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$8\times10=80$

is in the ones place, so we multiply by .

$7\times1=7$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$3\times\frac{1}{10}=.3$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$7\times\frac{1}{100}=.07$

is in the thousandths place, so we will multiply by $\frac{1}{1000}$ .

$6\times\frac{1}{1000}=.006$

Then we add the products together.

$\frac{\begin{array}[b]{r}80.000\7.000\ +\ .300\ .070\.006 \end{array}}{ \ \ \space87.376}$

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Question

What is in expanded form?

Tap to reveal answer

Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$9\times10=90$

is in the ones place, so we multiply by .

$4\times1=4$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$2\times\frac{1}{10}=.2$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$1\times\frac{1}{100}=.01$

is in the thousandths place, so we will multiply by $\frac{1}{1000}$ .

$8\times\frac{1}{1000}=.008$

Then we add the products together.

$\frac{\begin{array}[b]{r}90.000\4.000\ +\ .200\ .010\.008 \end{array}}{ \ \ \space94.218}$

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Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

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Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $40\ \text{workers}$ .

The factory will need $16\ \text{managers}$ .

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Question

At a car production company, manufacturers place tires and transmission on every car in the production line. A manager orders tires, how many transmissions should he order?

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Answer

In order to solve this problem we must make a table of ratios. In the question we are given the base ratio:

$4\ \text{tires}:1\ \text{transmission}$

We can use this ratio to make a table.

According to the table, the manager should order $4\ \text{transmissions}$ .

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Question

What is in expanded form?

$2\times10+7\times1+1\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)$

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Answer

When we write a number in expanded form, we multiply each digit by its place value.

is in the tens place, so we multiply by .

$2\times10=20$

is in the ones place, so we multiply by .

$7\times1=7$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$1\times\frac{1}{10}=.1$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$6\times\frac{1}{100}=.06$

Then we add the products together.

$\frac{\begin{array}[b]{r}20.00\7.00\ +\ .10\ .06 \end{array}}{ \ \ \space27.16}$

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Question

Sal is going to the fair with his family. He has $18.00 to buy tickets. How many tickets can he buy if each one costs $2.25?

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Answer

Divide the total amount of money he has by the cost of one ticket: $18\div 2.25=8$

Answer: Sal can buy 8 tickets at the fair.

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Question

At a car production company, manufacturers place tires and transmission on every car in the production line. A manager orders tires, how many transmissions should he order?

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Answer

In order to solve this problem we must make a table of ratios. In the question we are given the base ratio:

$4\ \text{tires}:1\ \text{transmission}$

We can use this ratio to make a table.

According to the table, the manager should order $8\ \text{transmissions}$ .

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Question

Ninety-six people must form eight equal groups. How many people will be in each group?

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Answer

Divide: $96\div 8=12$

Answer: There will be 12 people in each group.

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