TT7 lessons 54&55

Budgets are important

Another place we commonly run into fractions is in budgeting. Often companies will allocate a budget for advertising. This might then get split into 2 or more different categories. Sometimes, the proportions are balanced (each department gets the same amount). At other times, they might be unbalanced.

Example:

Company A has allocated 1/5 of its advertising budget to product A and 2/3 to product B. What fraction of the budget is allocated to these two products?

To answer this question, we add the fractions. But don't forget to find a common denominator!

Gadget Mania Incorporated is doing a national advertising campaign for its top three products, the diaper alarm, the singing doorbell, and the pain-free tummy toner. The advertising director wants to spend 1/8 of their advertising budget on the alarm, 1/4 on the doorbell, and 1/3 on the toner. What fraction of their advertising budget will they spend on those three products?

If Gadget Mania Incorporated allocates $2,400,000 to its advertising budget, how much will be spent on the three products listed?

To find out how much is to be spent on product A, B and C, we multiply each fraction by the total budget and then add those amounts together to find out how much will be spent on the 3 products together.

If you don't want to write out the factor lists or factor trees for many numbers, you can just multiply all the denominators together. However, this won't always give you the Least Common Denominator. You might have to do a bit of reduction at the end of the problem.

Carpentry is another common area to find fractions, proportions and percentages.

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Lesson 55

In the US, a 2x4 board does not actually measure 2 inches by 4 inches. This is because the boards are cut from green wood and then have to be dried and planed (evened out). Both of these actions reduce the dimensions of the board down to about 1.5 x 3.5 inches. This is true for all board sizes.
Also, historically a 2x4 DID measure 2x4 inches when finished, but to get more boards from each log, mills began to reduce the dimensions of the "green" cut.

The penny system for measuring nails dates back to the MIddle Ages? In England, pennies were sold by the 120 count. Larger nails were more expensive. On the low end, 1-inch nails were sold for 2 pence per 120 nails. That’s how 2-penny or 2d came to describe nails that are 1 inch in length. On the high end, six-inch nails were sold for about 60 pence per 120 nails, which is why 60-penny or 60d nails refer to 6-inch nails today.

Example problem

To be secure, a nail must go 2/3 of the way through the material and not poke out the back.

If you are nailing 1/2 inch plywood board to a 2x4 (1.5x3.5), how long of a nail do you need?

Mitch was building a doghouse for his dog, Rufus. He was using 2x4s to frame the house and needed to drive a nail through two 2x4s. What length of nail should he use?

1. This week: Lessons 54, 55 and chapter quiz.

   Math lab today from 2:30-3:30

Have a great holiday! See you in January