Arithmetic Practice

Break the number into the value of each digit:

This matches the thousands, hundreds, ones, tenths, and hundredths places.

Compare the numbers on a number line. Since $-3$ is to the right of $-8$, it is greater.

Absolute value is distance from zero, so it is always nonnegative.

Add by place value:

Write $6$ and carry $1$.

Write $5$ and carry $1$.

So,

Line up the decimal points:

Add:

Regroup because $0 < 8$.

Now subtract by place value:

So,

Multiply directly or think of repeated addition:

Find the number that times $7$ gives $42$:

So,

Follow the order of operations.

First evaluate the parentheses:

Then multiply:

Finally subtract:

Check whether $29$ has any factors besides $1$ and itself. It is not divisible by $2$, $3$, or $5$, so its only positive factors are $1$ and $29$.

Therefore, $29$ is prime.

First add the first two numbers:

Then subtract $4$:

So the value is $1$.

List the factors:

The largest factor they share is $6$.

So,

Convert the fraction to a decimal:

Now add:

Multiply numerators and denominators:

Simplify:

Divide miles by hours:

So the unit rate is $60$ miles per hour.

Cross multiply:

Divide by $5$:

Round to nearby easy numbers:

Estimate:

Now compute exactly:

The estimate is close to the exact value.

Evaluate each root:

and

Add the results:

Multiply the original length by the scale factor:

So the new length is $12$ cm.

Use the formula $I=Prt$:

The interest is $\$54$. The total amount is

So the total is $\$504$.

Find $15\%$ of $80$:

Add the increase to the original price:

The new price is $\$92$.

Multiply $7.4$ by $100{,}000$:

Divide to find the number of full packs:

This means there are $11$ full packs and $7$ pencils left over.

Follow the order of operations.

First evaluate the parentheses:

Then the exponent:

Now multiply:

Evaluate the other exponent and root:

Finish by adding and subtracting:

First find the $20\%$ increase:

So the new price is

Now find the $10\%$ decrease of $60$:

Subtract:

The final price is $\$54$.

Convert the fractions to decimals:

and

Now calculate:

Estimate by rounding $4.5$ to $5$:

Now compute exactly:

So the exact product is