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Victor is building a set of stairs. The board he is cutting to make the steps is 12 ft long. Each step is 3 1/2 feet long. How many complete steps can he make from th 12 ft board?

Does the word complete mean in a word problem? What does how much and How mant tell me to do?

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3 Answers

Hi Victor,

            One of the things I often recommend in a word problem concerning fractions is to temporarily replace them with whole numbers just to get a more relatable problem.  This often helps with the question of what operation do I do (add?, subtract?, multiply?, divide?).

             ex.  original problem is :

Victor is building a set of stairs. The board he is cutting to make the steps is 12 ft long. Each step is 3 1/2 feet long. How many complete steps can he make from th 12 ft board?

 

             an example of a whole number problem:

Victor is building a set of stairs. The board he is cutting to make the steps is 12 ft long. Each step is 5 feet long. How many complete steps can he make from th 12 ft board?

 

The how to is basically the same as I've seen in other responses.  You can use the take away method thinking of how many full steps you could cut off from the original 12 foot board.  Or you can use the division method finding how many times the 5 will divide into the 12 ( or how many 5 foot pieces the 12 foot board will divide into).  But my response is moreso of a method that I have often found helpful ( to myself as well as others) when trying to determine what to do....ie add, subtract, multiply or divide when fractions are involved. 

Hope this helps....I'm sure this will not be the only word problem with fractions you will encounter.

Lyn

First let's work out the problem, which gives you the following information:

     => you have a board that is 12 feet long to use to make the steps for the set of stairs

     => each step is 3.5 (or, 3 1/2) feet long

  To see how this problem plays out, imagine cutting the first 3.5 foot long step. Now you are left with a board that is 8.5 feet long (12 ft - 3.5 ft = 8.5 ft). Then you cut the second 3.5 foot long step, and are thus left with 5 feet (8.5 ft - 3.5 ft = 5 ft). Cutting the next 3.5 foot long step leaves you with 1.5 feet (5 ft - 3.5 ft = 1.5 ft). Since you are now left with a board that is 1.5 feet long, you cannot make another "complete" step that is 3.5 feet long like the others. Thus, from a 12 foot long board you can only make 3 complete steps which are 3.5 feet in length and you are left with a remainder of a 1.5 foot long board. That is what the word "complete" is referring to in the context of this question.

An easier way of doing the math behind this is by simply dividing the 12 foot long board by the desired length of each step, which is 3.5 feet long....

... i.e.,    12 ft / 3.5 ft = 3.42857 ≈ 3.4

    If you separate this yield of 3.4 into 3 and 0.4 ( 3 + 0.4 = 3.4 ), you find that you can make 3 whole or complete steps and one incomplete or a fraction of a step.

Shawnae, 

The word complete lets you know that they want only whole stair boards, not half of a stair board. Imagine looking up a stair case and seeing only half of a step. 

I am a visual learner so I would suggested taking a ruler because it is 12 inches long and figuring out how many times you can get exactly 3 1/2 inches. If you have less than 3 1/2 left over that is an incomplete stair and therefore scrap wood. 

You may also figure out the problem by determing who many times 3 1/2 goes into 12. 

Hope this helps.

Christie