512: Factory Ratios 3

We started with this:

In a factory, the ratio of men to women is 2:3. The ratio of right-handed men to left-handed men is 7:3. The ratio of right-handed women to left-handed women is 11:1. What fraction of the factory workforce is right-handed?
And then we extended with: What is the fewest number of employees possible in this building?

If the ugly-sweater party was held in that factory with the minimum number of workers possible and the  ratio of red to green ugly sweaters was 7:13, how likely is it that a left-handed man wore a red ugly sweater?

Source:

New GCSE Maths question: Ratio and proportion is the buzz thing! How are your students going to tackle it? pic.twitter.com/RyPsmc9z4m

— m4ths.com (@m4thsdotcom) December 16, 2015

510: Factory Ratios 1

In a factory, the ratio of men to women is 2:3.
The ratio of right-handed men to left-handed men is 7:3
The ratio of right-handed women to left-handed women is 11:1

What fraction of the factory workforce is right-handed?


Source:

New GCSE Maths question: Ratio and proportion is the buzz thing! How are your students going to tackle it? pic.twitter.com/RyPsmc9z4m

— m4ths.com (@m4thsdotcom) December 16, 2015

480: Percent Blue

What percent is orange? Green? pic.twitter.com/spmu8rewQH

— Dan Anderson (@dandersod) July 8, 2015

474: Fractional Understanding

What insights does a student need to have before this problem is solvable?

456: A and B

The problem speaks for itself.

A nice pair of questions from @pdaro. What do you think your students will say? #mathchat pic.twitter.com/mLtGRZei3O

— David Wees (@davidwees) May 10, 2015

454: Fraction Sum

Seems like a tough problem.

"Wait a minute. That would make it easier ..."

 source.

450: One-third of a triangle

You've been asked to shade one-third of this triangle.

And how do you know?
Here's a response:

• Is this a valid way to get one-third of the triangle?
• Does this technique require that we stipulate a right triangle?
• Does this technique require that we stipulate an isosceles one?
• Do the lines have to be parallel to each other?
• Do the lines have to be parallel to a side for this to work? 
• Perpendicular to a side for this to work?

• How might we generalize this method (if it can be generalized)?

sources:

Try to shade 1/3 of this triangle. How do you know it is 1/3? #mathchat #elemmathchat pic.twitter.com/KaLtPglBfV

— David Wees (@davidwees) May 2, 2015

@davidwees this may be more than you want pic.twitter.com/Azlkv1kwAw

— David Sawtelle (@davesawtelle) May 2, 2015

449: Fractions

The sum of ¼ and a number is equal to the product of ¼ and the number.
(a) Explain why the number must be negative.
(b) What's the number ?

source:

The sum of 1/4 and a number = the product of 1/4 and the number. (a) Explain why the # must be negative. (b) # ? #mathchat #SATprep #math

— David Marain (@dmarain) May 2, 2015

447: Shading a Square

Q1: How many different ways are there to shade this to show ¼?
Q2: How might kids shade this to show ¼?

Source:

Q1: How many different ways are there to shade this to show ¼? Q2: How might kids shade this to show ¼?  pic.twitter.com/vntk6kcYw7
— David Wees (@davidwees) April 25, 2015

406: Bracketology

Here are my three brackets:

Which of these is most useful in determining how many people are playing?

How jealous are you right now?

389: Talking Points - Fractions and Decimals

Always, Sometimes, Never?

Source.

362: Adding Fractions Again

How can we approach this beast of a problem without finding LCM?

$\dfrac{1}{1} - \dfrac{5}{6} + \dfrac{7}{12} - \dfrac{9}{20} + \dfrac{11}{30} - \dfrac{13}{42} + \dfrac{15}{56} - \dfrac{17}{72} + \dfrac{19}{90} = \dfrac{a}{b}$

262: Fractions by hand

You don't need a calculator for this one either. Why not?

Source: UVM, 2011

234: Fraction Manipulation

I know how I would solve this problem, but not everyone is comfortable with algebra. Which ways can you come up with? Which seems the best to you?

There is a number such that, when it is subtracted from the numerator of the fraction $\dfrac{5323}{7577}$ and added to the denominator, the fraction reduces to $\dfrac{17}{83}$. Determine the number.

203: Gotta be a fraction, right?

Is this thing rational?

189: Strasbourg Cathedral

Find the visual fractions.
Discuss the geometrical constructions the builder would have employed if he were limited to the following tools: a straight iron rod of 16.5 feet, string and a piece of chalk.

169: Quick Fractions

Explain whether 4/3 or 3/4 is closer to 1, and how you know.

96: Flower Petals

What fraction of this is yellow?

What fraction is yellow? How did you see it? pic.twitter.com/Y7OYAnkIgb
— Learning Maths (@LearningMaths) April 13, 2014

91: One-Quarter Times One-Quarter

What is one-quarter times one-quarter?

What if we look at things this way? Do we get the same results if we consider these as overlapping squares or as L-shaped pieces?

90: One-Quarter plus One-Quarter

Rob McDuff asks:

What is one-quarter plus one-quarter?