Can You Do These 5th-Grade Math Problems in Your Head?

Monica Lee

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Young brains are flexible and quick to adapt. And when it comes to good imaginations, they have it down pat. So they know how to imagine a math problem and complete it in their heads. How about you? Can you put down the pencil and calculator and do these math problems using brain power?

Do you recall all the tricks to help you choose the correct answer? You know, like rounding up or down numbers to help you get a general sense of the probable answer. With that in mind, you look at the options and narrow down the choices by trying just a single one (or two if needed) of the answers to select the correct one. Then there's the trick of reducing the fractions to their lowest multiple to make them easier to work with, within an equation.

But this is all kid's stuff, right? You know your multiplication tables, division, addition, subtraction, fraction, decimals and can stand tall against the dreaded story problems. No problem. But if you stumble a bit, don't feel bad; these kids spend a lot of their day on this, and you're only spending five minutes. So take the quiz and see how you do. We promise not to tell any fifth graders your score.

Put your pencil down and add this in your head. 13 + 8 = ?

Add the single digits together first to get 11. Then carry the one to get a "2" in the 10's place and a "1" in the one's place.

How's your subtraction? What is 54 - 23 = ?

This one is easy to do in your head. Subtract the single digits of both numbers to get 3-2 =1 and subtract the double digits or 5-2 =3. So the answer is 31.

Let see how easily you can divide in your head. 15 ÷ 3 = ?

This should have been easy because 3 x 5 = 15, so 3 goes into 15 five times.

Now onto multiplication. What is 22 X 4 = ?

These types of math problems are easy to do in your head when you don't need to carry numbers into the next column. The answer is 88.

Time for a word problem. A painter charges \$225 for materials and \$35 per hour for labor. The total cost of painting an office is \$330. How many hours did it take the painter to paint the office?

First reduce the amount so it's just labor by taking out the cost of supplies or \$330 - \$225 = \$105. Then divide the total cost of labor by the cost per hour or \$35 to get \$105 ÷ \$35 = 3 hours

How are your skills with fractions? What is 7/8 - 2/8 = ?

As long as you have a common denominator, you can subtract the two numerators and leave the denominator as is.

How's your decimal work? What is 143.9 - 23.2?

Be sure to remember where to keep the decimal point. That tip will come in handy later on.

It's getting harder. List the prime factors for the number 68. Which one is the correct answer?

Divide the number until you can't divide anymore. The result will be lots of small numbers and a prime number or the smallest non-prime number.

A team of 7 construction workers worked together to build 3 sheds in 10 days. How much of a shed did each of them build?

The 10 days is an added fact that doesn't help solve the problem. There are 3 sheds built and 7 workers, so each worker built 3/7 of a shed.

This is an easy one, right? 2.8 X 1000 = ?

There are three zeros in one thousand. So move the decimal three places to the right to get the correct answer.

How many minutes are in one week?

There are 60 minutes in an hour, and 24 hours in a day. So it's easier to multiply 24 x 6 = 144 and then add the 0 at the end to get 1,440. Next, multiply those minutes by 7 to get 10,080.

Okay, we warned you. This one was easy but the next is now harder. What's 113 + 49 = ?

Here is an example of how it's easier to add 50 rather than 49. So take 1 from 113 to make 112 and add that 1 to 49. The new, easier-to-add equation is 112 + 50 = 162.

Round the number 8,755 to the nearest 100. What is the answer?

As a refresher, you round up with a "5". Also the 100 place is the third place to the left of the decimal point so 755 will be 800. So the answer is 8,800.

Can you visualize this in your head? What is 678 - 98 = ?

Imagining the 8 subtracted by 8 is easy. But subtracting the 9 from 7 might have been a little harder. Too easy for you? Hang in there. This quiz gets progressively harder.

Justin can walk 4 kilometers in one hour. How long does it take him to walk 18 kilometers?

Justin walks 4 kilometers an hour. So in 4 hours, he walks 16 kilometers (4 x 4 = 16) But he needs to walk 18 kilometers, so there are 2 kilometers left to walk at 4 kilometers an hour, or 2/4 which can be reduced to 1/2 hour. So the answer is 4.5 hours.

Ready for more multiplication? Try this. 17 X 20 = ?

The easiest way to do this in your head is to multiply 2 x 17 = 34. Then add a zero to the sum to get 340.

Fractions again. 24/36 - 6/9 = ?

This problem is all about reducing until you have the lowest common denominator. First, divide both numerator and denominator by 3 to get 8/12 - 2/3. Now reduce the first fraction by dividing top and bottom by 4, so you have 2/3. The final equation is 2/3 -2/3 = 0

Make these into equivalent fractions, 44/100 = 176/a = 220/b What are "a" and "b"?

Ask yourself how many times does 44 go into 176; the answer is 4, which you need to multiply the denominator by to get 400. The same operation is used in the second equivalency equation.

Herb can eat a quarter of a pizza in one minute. How long does it take Herb to eat one pizza and a half?

Convert a pizza and a half into quarters. (4 quarters = 1) So 6 quarters = a pizza and a half. Then, one quarter = 1 minute to be eaten, so 6 quarters = 6 minutes to eat.

Find the quotient with remainder for the equation 93 divided by 5. What is the answer?

The number 93 when divided by 5 is 18 with a remainder of 3. When you divide 3.0 by 5 you get .6. So the answer is 18.6.

A quick decimal question. What is 14.75 - 5.26 = ?

Now remember, no calculator allowed. (But we won't tell if you used a #2 pencil.) Just keep the decimals where they are and do the subtraction to get the right answer.

How about this fractions problem? 14/42 - 15/75 = ?

Reduce the fractions to make them manageable. 14/42 = 1/3, and 15/75 = 1/5. So the equation now reads 1/3 - 1/5 = ? So cross multiply to get the common denominator or 5/15 - 3/15 = 2/15.

Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have?

If x = toys, then Bob has (5 + x) and Tom has x. Put this into an equation so that (5 + x) + x = 49. Subtract 5 from each side of the equation and get x + x = 44 or 2x = 44 or x = 22. Put x back into the equation and Bob has 27 and Tom has 22.

How good are you at converting fractions to decimals? Try this on for size. 16/128 + 15/24 = ?

Reducing the fractions you get 1/8 + 5/8 = 6/8 then reduce the answer to 3/4 or .75. It's all about reducing numbers until they are easier to work with in your head.

Another equation for you. What is 3.14 x 10 = ?

The decimal sign moves to the right one place when the number is multiplied by 10.

Linda bought 3 candy bars at \$1.20 each; a magazine for \$1.50 and a bottle of water for \$1.70. How much did Linda spend?

Linda bought 3 notebooks at \$120 each or \$3.60 in total. The magazine and water together cost \$3.20. So the total of \$3.60 + \$3.20 is \$6.80.

Round the number 5,932 to the nearest 10. What is the answer?

As a refresher, the first place to the left of the decimal point is "1" or single digits, the second place to the left of the decimal point is "10's" so the question asks you to round (down) to the nearest 10. So 32 would become 30.

Convert .6 to a fraction and simplify if possible. What's the answer?

The decimal .6 is the same as the fraction 6/10. This fraction can be reduced to 3/5 by dividing the numerator and denominator by 2.

Let's see how you do with division at this level. 78 ÷ 13 = ?

Whenever it gets complicated, look at the answers and see if you can find it. If you tried "5" the answer would have been 5 x 13 which is 65, which is too low. Then try the next higher number to see if that solves the problem.

A four-story building is 29 feet tall. Between which two whole numbers does the height of each story lie?

To find out the height of each floor divide 4 into 29 to get 7.25, so the whole number would be between 7 feet and 8 feet.

List the prime factors for the number 116. Which one is the correct answer?

Do you recall how to factor? You keep dividing the number until you can't divide anymore. The result will be lots of small numbers and a prime number or the smallest non-prime number.

An equivalency equation: 2/3 = x/30 = y/12. What is x and y?

Since 3 x 10 = 30, you know you have to multiply the numerator, 2 by 10 as well to get an equivalent fraction. The same operation is used in the second equivalency equation.

An old building was demolished. 5 dump trucks are used to transport a total of 2 tons of rubble. How much rubble did each truck carry?

Two tons were taken away by 5 trucks, so each one carried 2/5 of rubble. No pencil or calculator needed!

Find the quotient with remainder for the equation 45 divided by 4. What's the answer?

Since 11 x 4 = 44, we know the answer is 11 plus a remainder of 1. Now divide 4 into 1.0 and get .25. So the answer is the whole number 11 plus the decimal .25 or 11.25.

Last one! Convert .48 to a fraction and simplify if possible. What's the answer?

The decimal .48 can be expressed as 48/100. Once simplified by dividing by 4, the fraction becomes 12/25.