cutting a stick

Can you solve this problem?

1/8 of a stick is cut off. If If another stick that is 15 inches long is glued to the remaining part of the first stick, the first stick will be 1/2 longer than its original length. What is the original length of the first stick?

In this problem, you need to find the match between the fractional part and the amount in it ( if you do not know about these terms, please go to Word Problem: Detailed Explanations of Reasoning and Solving Strategies Volumes 11-A, 11-B and 12)

15 inches  not only has covered  1/8 of the stick that is cut off but also makes the  the stick 1/2 longer so we can say that 15 inches match the sum of the fractional parts: 1/8 and 1/2.

We divide the sum of the fractional parts: 1/8+1/2=5/8 into the amount that matches it: 15 inches to find the amount in 1, which is the length of the original stick: ( please go to the books Word Problem: Detailed Explanations of Reasoning and Solving Strategies Volumes 11-A, 11-B and 12 for more detailed explanation):

15÷5/8=24 inches

The original stick is 24 inches. 

 

multiplications with 0’s in the end of the factors and products

Look at the following equations:

1. 70 x 4=280

2. 70 x 40=2,800

3. 700 x 4=2,800

4. 700 x 40=28,000

5. 7,000 x 40=280,000

What can we learn from the above equations?

All the equations have four numbers in common: 7 , 4 , their products, 28 and 0’s.

Here is the trick: when you try to get the answer of 7,000 x 40, you only need to take two steps:

First: Find the product of 7 and 4, which is 28;

Secondly: count the number of 0’s in both 7,000 and 40, which is 4; put the four 0’s after 28.

Therefore, the product of 7,000 and 40 is 280,000

The last thing that you want to do is to multiply 0’s by 0’s in the numbers.